Properties

Label 600.2.b.h.251.6
Level $600$
Weight $2$
Character 600.251
Analytic conductor $4.791$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [600,2,Mod(251,600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("600.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.537291533250985984.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 5x^{10} + 14x^{8} - 30x^{6} + 56x^{4} - 80x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.6
Root \(0.847808 - 1.13191i\) of defining polynomial
Character \(\chi\) \(=\) 600.251
Dual form 600.2.b.h.251.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.847808 + 1.13191i) q^{2} +(0.242431 - 1.71500i) q^{3} +(-0.562443 - 1.91929i) q^{4} +(1.73569 + 1.72840i) q^{6} -3.08957i q^{7} +(2.64930 + 0.990551i) q^{8} +(-2.88245 - 0.831539i) q^{9} +O(q^{10})\) \(q+(-0.847808 + 1.13191i) q^{2} +(0.242431 - 1.71500i) q^{3} +(-0.562443 - 1.91929i) q^{4} +(1.73569 + 1.72840i) q^{6} -3.08957i q^{7} +(2.64930 + 0.990551i) q^{8} +(-2.88245 - 0.831539i) q^{9} +2.54654i q^{11} +(-3.42793 + 0.499295i) q^{12} -5.06696i q^{13} +(3.49711 + 2.61936i) q^{14} +(-3.36732 + 2.15898i) q^{16} +0.214179i q^{17} +(3.38500 - 2.55770i) q^{18} +2.60975 q^{19} +(-5.29861 - 0.749006i) q^{21} +(-2.88245 - 2.15898i) q^{22} -4.47647 q^{23} +(2.34107 - 4.30342i) q^{24} +(5.73534 + 4.29581i) q^{26} +(-2.12489 + 4.74182i) q^{27} +(-5.92976 + 1.73770i) q^{28} -7.86770 q^{29} +4.58758i q^{31} +(0.411070 - 5.64190i) q^{32} +(4.36732 + 0.617360i) q^{33} +(-0.242431 - 0.181582i) q^{34} +(0.0252553 + 5.99995i) q^{36} -7.67714i q^{37} +(-2.21257 + 2.95400i) q^{38} +(-8.68984 - 1.22839i) q^{39} -9.26946i q^{41} +(5.34001 - 5.36253i) q^{42} -11.4049 q^{43} +(4.88754 - 1.43228i) q^{44} +(3.79518 - 5.06696i) q^{46} +10.5972 q^{47} +(2.88630 + 6.29835i) q^{48} -2.54541 q^{49} +(0.367316 + 0.0519235i) q^{51} +(-9.72494 + 2.84987i) q^{52} -9.51198 q^{53} +(-3.56582 - 6.42533i) q^{54} +(3.06037 - 8.18520i) q^{56} +(0.632684 - 4.47572i) q^{57} +(6.67030 - 8.90553i) q^{58} -0.428357i q^{59} +1.11217i q^{61} +(-5.19273 - 3.88939i) q^{62} +(-2.56909 + 8.90553i) q^{63} +(6.03762 + 5.24854i) q^{64} +(-4.40144 + 4.42001i) q^{66} -2.35998 q^{67} +(0.411070 - 0.120463i) q^{68} +(-1.08523 + 7.67714i) q^{69} +6.12075 q^{71} +(-6.81281 - 5.05822i) q^{72} +12.0147 q^{73} +(8.68984 + 6.50874i) q^{74} +(-1.46783 - 5.00885i) q^{76} +7.86770 q^{77} +(8.75774 - 8.79468i) q^{78} -11.6319i q^{79} +(7.61709 + 4.79374i) q^{81} +(10.4922 + 7.85873i) q^{82} +2.29913i q^{83} +(1.54261 + 10.5908i) q^{84} +(9.66919 - 12.9094i) q^{86} +(-1.90737 + 13.4931i) q^{87} +(-2.52248 + 6.74655i) q^{88} -12.4853i q^{89} -15.6547 q^{91} +(2.51776 + 8.59162i) q^{92} +(7.86770 + 1.11217i) q^{93} +(-8.98440 + 11.9951i) q^{94} +(-9.57620 - 2.07276i) q^{96} +8.04496 q^{97} +(2.15802 - 2.88118i) q^{98} +(2.11755 - 7.34028i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9} - 3 q^{12} - 6 q^{16} - 5 q^{18} - 4 q^{19} - 2 q^{22} + 5 q^{24} + 8 q^{27} - 20 q^{28} + 18 q^{33} - 2 q^{34} + 19 q^{36} - 14 q^{42} - 40 q^{43} - 16 q^{46} - 27 q^{48} - 36 q^{49} - 30 q^{51} - 4 q^{52} - 30 q^{54} + 42 q^{57} + 52 q^{58} + 10 q^{64} + 7 q^{66} - 60 q^{67} - 39 q^{72} + 12 q^{73} - 38 q^{76} + 54 q^{78} - 10 q^{81} + 58 q^{82} - 34 q^{84} + 34 q^{88} - 24 q^{91} + 28 q^{94} - 31 q^{96} - 32 q^{97} + 58 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.847808 + 1.13191i −0.599491 + 0.800382i
\(3\) 0.242431 1.71500i 0.139968 0.990156i
\(4\) −0.562443 1.91929i −0.281221 0.959643i
\(5\) 0 0
\(6\) 1.73569 + 1.72840i 0.708593 + 0.705617i
\(7\) 3.08957i 1.16775i −0.811845 0.583873i \(-0.801537\pi\)
0.811845 0.583873i \(-0.198463\pi\)
\(8\) 2.64930 + 0.990551i 0.936670 + 0.350213i
\(9\) −2.88245 0.831539i −0.960818 0.277180i
\(10\) 0 0
\(11\) 2.54654i 0.767810i 0.923373 + 0.383905i \(0.125421\pi\)
−0.923373 + 0.383905i \(0.874579\pi\)
\(12\) −3.42793 + 0.499295i −0.989558 + 0.144134i
\(13\) 5.06696i 1.40532i −0.711525 0.702661i \(-0.751995\pi\)
0.711525 0.702661i \(-0.248005\pi\)
\(14\) 3.49711 + 2.61936i 0.934642 + 0.700053i
\(15\) 0 0
\(16\) −3.36732 + 2.15898i −0.841829 + 0.539744i
\(17\) 0.214179i 0.0519459i 0.999663 + 0.0259730i \(0.00826838\pi\)
−0.999663 + 0.0259730i \(0.991732\pi\)
\(18\) 3.38500 2.55770i 0.797851 0.602855i
\(19\) 2.60975 0.598717 0.299359 0.954141i \(-0.403227\pi\)
0.299359 + 0.954141i \(0.403227\pi\)
\(20\) 0 0
\(21\) −5.29861 0.749006i −1.15625 0.163447i
\(22\) −2.88245 2.15898i −0.614541 0.460295i
\(23\) −4.47647 −0.933408 −0.466704 0.884414i \(-0.654559\pi\)
−0.466704 + 0.884414i \(0.654559\pi\)
\(24\) 2.34107 4.30342i 0.477869 0.878431i
\(25\) 0 0
\(26\) 5.73534 + 4.29581i 1.12479 + 0.842478i
\(27\) −2.12489 + 4.74182i −0.408934 + 0.912564i
\(28\) −5.92976 + 1.73770i −1.12062 + 0.328395i
\(29\) −7.86770 −1.46100 −0.730498 0.682915i \(-0.760712\pi\)
−0.730498 + 0.682915i \(0.760712\pi\)
\(30\) 0 0
\(31\) 4.58758i 0.823953i 0.911194 + 0.411977i \(0.135161\pi\)
−0.911194 + 0.411977i \(0.864839\pi\)
\(32\) 0.411070 5.64190i 0.0726676 0.997356i
\(33\) 4.36732 + 0.617360i 0.760252 + 0.107469i
\(34\) −0.242431 0.181582i −0.0415766 0.0311411i
\(35\) 0 0
\(36\) 0.0252553 + 5.99995i 0.00420921 + 0.999991i
\(37\) 7.67714i 1.26211i −0.775736 0.631057i \(-0.782621\pi\)
0.775736 0.631057i \(-0.217379\pi\)
\(38\) −2.21257 + 2.95400i −0.358925 + 0.479202i
\(39\) −8.68984 1.22839i −1.39149 0.196700i
\(40\) 0 0
\(41\) 9.26946i 1.44765i −0.689985 0.723823i \(-0.742383\pi\)
0.689985 0.723823i \(-0.257617\pi\)
\(42\) 5.34001 5.36253i 0.823981 0.827457i
\(43\) −11.4049 −1.73924 −0.869618 0.493725i \(-0.835635\pi\)
−0.869618 + 0.493725i \(0.835635\pi\)
\(44\) 4.88754 1.43228i 0.736824 0.215925i
\(45\) 0 0
\(46\) 3.79518 5.06696i 0.559569 0.747082i
\(47\) 10.5972 1.54576 0.772881 0.634551i \(-0.218815\pi\)
0.772881 + 0.634551i \(0.218815\pi\)
\(48\) 2.88630 + 6.29835i 0.416602 + 0.909089i
\(49\) −2.54541 −0.363631
\(50\) 0 0
\(51\) 0.367316 + 0.0519235i 0.0514346 + 0.00727075i
\(52\) −9.72494 + 2.84987i −1.34861 + 0.395206i
\(53\) −9.51198 −1.30657 −0.653285 0.757112i \(-0.726610\pi\)
−0.653285 + 0.757112i \(0.726610\pi\)
\(54\) −3.56582 6.42533i −0.485247 0.874377i
\(55\) 0 0
\(56\) 3.06037 8.18520i 0.408960 1.09379i
\(57\) 0.632684 4.47572i 0.0838010 0.592823i
\(58\) 6.67030 8.90553i 0.875853 1.16935i
\(59\) 0.428357i 0.0557674i −0.999611 0.0278837i \(-0.991123\pi\)
0.999611 0.0278837i \(-0.00887680\pi\)
\(60\) 0 0
\(61\) 1.11217i 0.142399i 0.997462 + 0.0711995i \(0.0226827\pi\)
−0.997462 + 0.0711995i \(0.977317\pi\)
\(62\) −5.19273 3.88939i −0.659477 0.493953i
\(63\) −2.56909 + 8.90553i −0.323675 + 1.12199i
\(64\) 6.03762 + 5.24854i 0.754702 + 0.656068i
\(65\) 0 0
\(66\) −4.40144 + 4.42001i −0.541780 + 0.544065i
\(67\) −2.35998 −0.288317 −0.144159 0.989555i \(-0.546048\pi\)
−0.144159 + 0.989555i \(0.546048\pi\)
\(68\) 0.411070 0.120463i 0.0498495 0.0146083i
\(69\) −1.08523 + 7.67714i −0.130647 + 0.924219i
\(70\) 0 0
\(71\) 6.12075 0.726399 0.363199 0.931711i \(-0.381684\pi\)
0.363199 + 0.931711i \(0.381684\pi\)
\(72\) −6.81281 5.05822i −0.802898 0.596117i
\(73\) 12.0147 1.40621 0.703106 0.711085i \(-0.251796\pi\)
0.703106 + 0.711085i \(0.251796\pi\)
\(74\) 8.68984 + 6.50874i 1.01017 + 0.756626i
\(75\) 0 0
\(76\) −1.46783 5.00885i −0.168372 0.574555i
\(77\) 7.86770 0.896608
\(78\) 8.75774 8.79468i 0.991619 0.995802i
\(79\) 11.6319i 1.30869i −0.756194 0.654347i \(-0.772943\pi\)
0.756194 0.654347i \(-0.227057\pi\)
\(80\) 0 0
\(81\) 7.61709 + 4.79374i 0.846343 + 0.532638i
\(82\) 10.4922 + 7.85873i 1.15867 + 0.867851i
\(83\) 2.29913i 0.252362i 0.992007 + 0.126181i \(0.0402720\pi\)
−0.992007 + 0.126181i \(0.959728\pi\)
\(84\) 1.54261 + 10.5908i 0.168312 + 1.15555i
\(85\) 0 0
\(86\) 9.66919 12.9094i 1.04266 1.39205i
\(87\) −1.90737 + 13.4931i −0.204492 + 1.44661i
\(88\) −2.52248 + 6.74655i −0.268897 + 0.719185i
\(89\) 12.4853i 1.32344i −0.749752 0.661719i \(-0.769827\pi\)
0.749752 0.661719i \(-0.230173\pi\)
\(90\) 0 0
\(91\) −15.6547 −1.64106
\(92\) 2.51776 + 8.59162i 0.262494 + 0.895738i
\(93\) 7.86770 + 1.11217i 0.815842 + 0.115327i
\(94\) −8.98440 + 11.9951i −0.926670 + 1.23720i
\(95\) 0 0
\(96\) −9.57620 2.07276i −0.977367 0.211550i
\(97\) 8.04496 0.816842 0.408421 0.912794i \(-0.366080\pi\)
0.408421 + 0.912794i \(0.366080\pi\)
\(98\) 2.15802 2.88118i 0.217993 0.291043i
\(99\) 2.11755 7.34028i 0.212821 0.737726i
\(100\) 0 0
\(101\) 1.08523 0.107985 0.0539924 0.998541i \(-0.482805\pi\)
0.0539924 + 0.998541i \(0.482805\pi\)
\(102\) −0.370187 + 0.371748i −0.0366539 + 0.0368085i
\(103\) 11.6319i 1.14613i 0.819511 + 0.573064i \(0.194245\pi\)
−0.819511 + 0.573064i \(0.805755\pi\)
\(104\) 5.01908 13.4239i 0.492162 1.31632i
\(105\) 0 0
\(106\) 8.06433 10.7667i 0.783277 1.04576i
\(107\) 6.50874i 0.629224i −0.949220 0.314612i \(-0.898126\pi\)
0.949220 0.314612i \(-0.101874\pi\)
\(108\) 10.2960 + 1.41126i 0.990736 + 0.135799i
\(109\) 5.06696i 0.485327i 0.970111 + 0.242663i \(0.0780210\pi\)
−0.970111 + 0.242663i \(0.921979\pi\)
\(110\) 0 0
\(111\) −13.1663 1.86118i −1.24969 0.176655i
\(112\) 6.67030 + 10.4035i 0.630284 + 0.983043i
\(113\) 6.05364i 0.569479i −0.958605 0.284739i \(-0.908093\pi\)
0.958605 0.284739i \(-0.0919070\pi\)
\(114\) 4.52972 + 4.51069i 0.424247 + 0.422465i
\(115\) 0 0
\(116\) 4.42513 + 15.1004i 0.410863 + 1.40203i
\(117\) −4.21337 + 14.6053i −0.389526 + 1.35026i
\(118\) 0.484862 + 0.363165i 0.0446352 + 0.0334320i
\(119\) 0.661719 0.0606597
\(120\) 0 0
\(121\) 4.51514 0.410467
\(122\) −1.25888 0.942908i −0.113973 0.0853668i
\(123\) −15.8971 2.24720i −1.43340 0.202624i
\(124\) 8.80487 2.58025i 0.790701 0.231713i
\(125\) 0 0
\(126\) −7.90217 10.4582i −0.703981 0.931687i
\(127\) 0.958763i 0.0850765i 0.999095 + 0.0425382i \(0.0135444\pi\)
−0.999095 + 0.0425382i \(0.986456\pi\)
\(128\) −11.0596 + 2.38428i −0.977542 + 0.210743i
\(129\) −2.76491 + 19.5595i −0.243437 + 1.72211i
\(130\) 0 0
\(131\) 3.78126i 0.330370i −0.986263 0.165185i \(-0.947178\pi\)
0.986263 0.165185i \(-0.0528221\pi\)
\(132\) −1.27147 8.72936i −0.110668 0.759793i
\(133\) 8.06299i 0.699149i
\(134\) 2.00081 2.67128i 0.172843 0.230764i
\(135\) 0 0
\(136\) −0.212155 + 0.567424i −0.0181921 + 0.0486562i
\(137\) 13.1878i 1.12671i 0.826215 + 0.563355i \(0.190490\pi\)
−0.826215 + 0.563355i \(0.809510\pi\)
\(138\) −7.76977 7.73713i −0.661407 0.658628i
\(139\) 17.2947 1.46692 0.733460 0.679733i \(-0.237904\pi\)
0.733460 + 0.679733i \(0.237904\pi\)
\(140\) 0 0
\(141\) 2.56909 18.1742i 0.216357 1.53055i
\(142\) −5.18922 + 6.92814i −0.435470 + 0.581396i
\(143\) 12.9032 1.07902
\(144\) 11.5014 3.42310i 0.958451 0.285258i
\(145\) 0 0
\(146\) −10.1861 + 13.5995i −0.843011 + 1.12551i
\(147\) −0.617087 + 4.36539i −0.0508965 + 0.360051i
\(148\) −14.7346 + 4.31795i −1.21118 + 0.354934i
\(149\) 3.81475 0.312516 0.156258 0.987716i \(-0.450057\pi\)
0.156258 + 0.987716i \(0.450057\pi\)
\(150\) 0 0
\(151\) 13.2235i 1.07611i 0.842909 + 0.538056i \(0.180841\pi\)
−0.842909 + 0.538056i \(0.819159\pi\)
\(152\) 6.91401 + 2.58509i 0.560800 + 0.209678i
\(153\) 0.178098 0.617360i 0.0143983 0.0499106i
\(154\) −6.67030 + 8.90553i −0.537508 + 0.717628i
\(155\) 0 0
\(156\) 2.52991 + 17.3692i 0.202555 + 1.39065i
\(157\) 6.56497i 0.523942i −0.965076 0.261971i \(-0.915628\pi\)
0.965076 0.261971i \(-0.0843725\pi\)
\(158\) 13.1663 + 9.86165i 1.04746 + 0.784550i
\(159\) −2.30600 + 16.3131i −0.182878 + 1.29371i
\(160\) 0 0
\(161\) 13.8303i 1.08998i
\(162\) −11.8839 + 4.55769i −0.933689 + 0.358086i
\(163\) 8.13957 0.637540 0.318770 0.947832i \(-0.396730\pi\)
0.318770 + 0.947832i \(0.396730\pi\)
\(164\) −17.7907 + 5.21354i −1.38922 + 0.407109i
\(165\) 0 0
\(166\) −2.60241 1.94922i −0.201986 0.151289i
\(167\) −21.8561 −1.69128 −0.845640 0.533754i \(-0.820781\pi\)
−0.845640 + 0.533754i \(0.820781\pi\)
\(168\) −13.2957 7.23289i −1.02578 0.558029i
\(169\) −12.6741 −0.974929
\(170\) 0 0
\(171\) −7.52248 2.17011i −0.575258 0.165952i
\(172\) 6.41462 + 21.8893i 0.489110 + 1.66905i
\(173\) −9.51198 −0.723182 −0.361591 0.932337i \(-0.617766\pi\)
−0.361591 + 0.932337i \(0.617766\pi\)
\(174\) −13.6559 13.5985i −1.03525 1.03090i
\(175\) 0 0
\(176\) −5.49792 8.57500i −0.414421 0.646365i
\(177\) −0.734633 0.103847i −0.0552184 0.00780562i
\(178\) 14.1322 + 10.5851i 1.05926 + 0.793389i
\(179\) 16.2398i 1.21382i 0.794771 + 0.606910i \(0.207591\pi\)
−0.794771 + 0.606910i \(0.792409\pi\)
\(180\) 0 0
\(181\) 9.74808i 0.724569i −0.932068 0.362284i \(-0.881997\pi\)
0.932068 0.362284i \(-0.118003\pi\)
\(182\) 13.2722 17.7197i 0.983800 1.31347i
\(183\) 1.90737 + 0.269625i 0.140997 + 0.0199312i
\(184\) −11.8595 4.43417i −0.874295 0.326891i
\(185\) 0 0
\(186\) −7.92918 + 7.96262i −0.581396 + 0.583848i
\(187\) −0.545414 −0.0398846
\(188\) −5.96033 20.3391i −0.434701 1.48338i
\(189\) 14.6502 + 6.56497i 1.06564 + 0.477531i
\(190\) 0 0
\(191\) 2.30600 0.166856 0.0834281 0.996514i \(-0.473413\pi\)
0.0834281 + 0.996514i \(0.473413\pi\)
\(192\) 10.4650 9.08211i 0.755243 0.655445i
\(193\) 11.2498 0.809776 0.404888 0.914366i \(-0.367310\pi\)
0.404888 + 0.914366i \(0.367310\pi\)
\(194\) −6.82058 + 9.10617i −0.489689 + 0.653785i
\(195\) 0 0
\(196\) 1.43165 + 4.88538i 0.102261 + 0.348956i
\(197\) 6.78247 0.483231 0.241615 0.970372i \(-0.422323\pi\)
0.241615 + 0.970372i \(0.422323\pi\)
\(198\) 6.51327 + 8.62002i 0.462878 + 0.612598i
\(199\) 0.632789i 0.0448573i −0.999748 0.0224286i \(-0.992860\pi\)
0.999748 0.0224286i \(-0.00713985\pi\)
\(200\) 0 0
\(201\) −0.572131 + 4.04736i −0.0403550 + 0.285479i
\(202\) −0.920070 + 1.22839i −0.0647359 + 0.0864291i
\(203\) 24.3078i 1.70607i
\(204\) −0.106938 0.734189i −0.00748718 0.0514035i
\(205\) 0 0
\(206\) −13.1663 9.86165i −0.917340 0.687093i
\(207\) 12.9032 + 3.72235i 0.896835 + 0.258722i
\(208\) 10.9394 + 17.0621i 0.758514 + 1.18304i
\(209\) 6.64582i 0.459701i
\(210\) 0 0
\(211\) 11.6400 0.801332 0.400666 0.916224i \(-0.368779\pi\)
0.400666 + 0.916224i \(0.368779\pi\)
\(212\) 5.34994 + 18.2562i 0.367436 + 1.25384i
\(213\) 1.48386 10.4971i 0.101672 0.719248i
\(214\) 7.36732 + 5.51817i 0.503619 + 0.377214i
\(215\) 0 0
\(216\) −10.3265 + 10.4577i −0.702628 + 0.711557i
\(217\) 14.1736 0.962168
\(218\) −5.73534 4.29581i −0.388447 0.290949i
\(219\) 2.91273 20.6052i 0.196824 1.39237i
\(220\) 0 0
\(221\) 1.08523 0.0730008
\(222\) 13.2692 13.3252i 0.890570 0.894326i
\(223\) 10.7667i 0.720992i −0.932761 0.360496i \(-0.882607\pi\)
0.932761 0.360496i \(-0.117393\pi\)
\(224\) −17.4310 1.27003i −1.16466 0.0848573i
\(225\) 0 0
\(226\) 6.85218 + 5.13233i 0.455800 + 0.341397i
\(227\) 12.8365i 0.851991i −0.904725 0.425996i \(-0.859924\pi\)
0.904725 0.425996i \(-0.140076\pi\)
\(228\) −8.94603 + 1.30303i −0.592465 + 0.0862956i
\(229\) 14.9684i 0.989143i −0.869137 0.494571i \(-0.835325\pi\)
0.869137 0.494571i \(-0.164675\pi\)
\(230\) 0 0
\(231\) 1.90737 13.4931i 0.125496 0.887781i
\(232\) −20.8439 7.79336i −1.36847 0.511659i
\(233\) 20.8980i 1.36908i −0.728977 0.684538i \(-0.760004\pi\)
0.728977 0.684538i \(-0.239996\pi\)
\(234\) −12.9597 17.1516i −0.847205 1.12124i
\(235\) 0 0
\(236\) −0.822140 + 0.240926i −0.0535167 + 0.0156830i
\(237\) −19.9488 2.81994i −1.29581 0.183175i
\(238\) −0.561011 + 0.749006i −0.0363649 + 0.0485509i
\(239\) 28.6386 1.85248 0.926239 0.376937i \(-0.123023\pi\)
0.926239 + 0.376937i \(0.123023\pi\)
\(240\) 0 0
\(241\) 9.24977 0.595830 0.297915 0.954592i \(-0.403709\pi\)
0.297915 + 0.954592i \(0.403709\pi\)
\(242\) −3.82797 + 5.11073i −0.246071 + 0.328530i
\(243\) 10.0679 11.9012i 0.645856 0.763460i
\(244\) 2.13457 0.625532i 0.136652 0.0400456i
\(245\) 0 0
\(246\) 16.0214 16.0889i 1.02148 1.02579i
\(247\) 13.2235i 0.841390i
\(248\) −4.54423 + 12.1539i −0.288559 + 0.771773i
\(249\) 3.94301 + 0.557380i 0.249878 + 0.0353225i
\(250\) 0 0
\(251\) 1.23472i 0.0779348i 0.999240 + 0.0389674i \(0.0124069\pi\)
−0.999240 + 0.0389674i \(0.987593\pi\)
\(252\) 18.5372 0.0780279i 1.16774 0.00491529i
\(253\) 11.3995i 0.716680i
\(254\) −1.08523 0.812847i −0.0680937 0.0510026i
\(255\) 0 0
\(256\) 6.67764 14.5399i 0.417352 0.908745i
\(257\) 18.6054i 1.16057i −0.814413 0.580286i \(-0.802941\pi\)
0.814413 0.580286i \(-0.197059\pi\)
\(258\) −19.7955 19.7123i −1.23241 1.22723i
\(259\) −23.7190 −1.47383
\(260\) 0 0
\(261\) 22.6783 + 6.54230i 1.40375 + 0.404958i
\(262\) 4.28005 + 3.20578i 0.264422 + 0.198054i
\(263\) 11.2589 0.694255 0.347128 0.937818i \(-0.387157\pi\)
0.347128 + 0.937818i \(0.387157\pi\)
\(264\) 10.9588 + 5.96163i 0.674469 + 0.366913i
\(265\) 0 0
\(266\) 9.12658 + 6.83586i 0.559586 + 0.419134i
\(267\) −21.4123 3.02682i −1.31041 0.185238i
\(268\) 1.32735 + 4.52947i 0.0810809 + 0.276681i
\(269\) 11.6824 0.712291 0.356146 0.934430i \(-0.384091\pi\)
0.356146 + 0.934430i \(0.384091\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −0.462407 0.721207i −0.0280375 0.0437296i
\(273\) −3.79518 + 26.8478i −0.229695 + 1.62490i
\(274\) −14.9274 11.1807i −0.901798 0.675452i
\(275\) 0 0
\(276\) 15.3450 2.23508i 0.923661 0.134536i
\(277\) 17.4252i 1.04698i −0.852032 0.523490i \(-0.824630\pi\)
0.852032 0.523490i \(-0.175370\pi\)
\(278\) −14.6626 + 19.5761i −0.879405 + 1.17410i
\(279\) 3.81475 13.2235i 0.228383 0.791669i
\(280\) 0 0
\(281\) 12.9736i 0.773941i −0.922092 0.386971i \(-0.873521\pi\)
0.922092 0.386971i \(-0.126479\pi\)
\(282\) 18.3935 + 18.3162i 1.09532 + 1.09072i
\(283\) −12.3893 −0.736470 −0.368235 0.929733i \(-0.620038\pi\)
−0.368235 + 0.929733i \(0.620038\pi\)
\(284\) −3.44257 11.7475i −0.204279 0.697084i
\(285\) 0 0
\(286\) −10.9394 + 14.6053i −0.646863 + 0.863628i
\(287\) −28.6386 −1.69048
\(288\) −5.87635 + 15.9207i −0.346267 + 0.938136i
\(289\) 16.9541 0.997302
\(290\) 0 0
\(291\) 1.95035 13.7971i 0.114331 0.808801i
\(292\) −6.75757 23.0596i −0.395457 1.34946i
\(293\) 31.7916 1.85729 0.928644 0.370973i \(-0.120976\pi\)
0.928644 + 0.370973i \(0.120976\pi\)
\(294\) −4.41806 4.39950i −0.257666 0.256584i
\(295\) 0 0
\(296\) 7.60460 20.3391i 0.442009 1.18219i
\(297\) −12.0752 5.41110i −0.700676 0.313984i
\(298\) −3.23417 + 4.31795i −0.187351 + 0.250132i
\(299\) 22.6821i 1.31174i
\(300\) 0 0
\(301\) 35.2363i 2.03099i
\(302\) −14.9678 11.2110i −0.861300 0.645119i
\(303\) 0.263094 1.86118i 0.0151144 0.106922i
\(304\) −8.78785 + 5.63438i −0.504017 + 0.323154i
\(305\) 0 0
\(306\) 0.547804 + 0.724994i 0.0313158 + 0.0414451i
\(307\) 10.3288 0.589495 0.294747 0.955575i \(-0.404764\pi\)
0.294747 + 0.955575i \(0.404764\pi\)
\(308\) −4.42513 15.1004i −0.252145 0.860423i
\(309\) 19.9488 + 2.81994i 1.13485 + 0.160421i
\(310\) 0 0
\(311\) 5.13819 0.291360 0.145680 0.989332i \(-0.453463\pi\)
0.145680 + 0.989332i \(0.453463\pi\)
\(312\) −21.8052 11.8621i −1.23448 0.671559i
\(313\) −15.6741 −0.885951 −0.442976 0.896534i \(-0.646077\pi\)
−0.442976 + 0.896534i \(0.646077\pi\)
\(314\) 7.43096 + 5.56584i 0.419353 + 0.314098i
\(315\) 0 0
\(316\) −22.3250 + 6.54230i −1.25588 + 0.368033i
\(317\) −8.95293 −0.502847 −0.251423 0.967877i \(-0.580899\pi\)
−0.251423 + 0.967877i \(0.580899\pi\)
\(318\) −16.5099 16.4405i −0.925827 0.921939i
\(319\) 20.0354i 1.12177i
\(320\) 0 0
\(321\) −11.1625 1.57792i −0.623030 0.0880710i
\(322\) −15.6547 11.7255i −0.872403 0.653435i
\(323\) 0.558952i 0.0311009i
\(324\) 4.91639 17.3156i 0.273133 0.961976i
\(325\) 0 0
\(326\) −6.90079 + 9.21326i −0.382199 + 0.510275i
\(327\) 8.68984 + 1.22839i 0.480549 + 0.0679300i
\(328\) 9.18188 24.5576i 0.506984 1.35597i
\(329\) 32.7408i 1.80506i
\(330\) 0 0
\(331\) −4.48486 −0.246510 −0.123255 0.992375i \(-0.539333\pi\)
−0.123255 + 0.992375i \(0.539333\pi\)
\(332\) 4.41268 1.29313i 0.242178 0.0709696i
\(333\) −6.38384 + 22.1290i −0.349832 + 1.21266i
\(334\) 18.5298 24.7392i 1.01391 1.35367i
\(335\) 0 0
\(336\) 19.4592 8.91743i 1.06158 0.486486i
\(337\) −25.9991 −1.41626 −0.708130 0.706082i \(-0.750461\pi\)
−0.708130 + 0.706082i \(0.750461\pi\)
\(338\) 10.7452 14.3459i 0.584461 0.780315i
\(339\) −10.3820 1.46759i −0.563873 0.0797085i
\(340\) 0 0
\(341\) −11.6824 −0.632640
\(342\) 8.83398 6.67494i 0.477687 0.360939i
\(343\) 13.7627i 0.743118i
\(344\) −30.2151 11.2972i −1.62909 0.609103i
\(345\) 0 0
\(346\) 8.06433 10.7667i 0.433541 0.578822i
\(347\) 10.7184i 0.575392i 0.957722 + 0.287696i \(0.0928892\pi\)
−0.957722 + 0.287696i \(0.907111\pi\)
\(348\) 26.9699 3.92831i 1.44574 0.210579i
\(349\) 11.6319i 0.622643i −0.950305 0.311322i \(-0.899228\pi\)
0.950305 0.311322i \(-0.100772\pi\)
\(350\) 0 0
\(351\) 24.0266 + 10.7667i 1.28245 + 0.574684i
\(352\) 14.3673 + 1.04681i 0.765781 + 0.0557949i
\(353\) 21.7547i 1.15789i 0.815367 + 0.578944i \(0.196535\pi\)
−0.815367 + 0.578944i \(0.803465\pi\)
\(354\) 0.740373 0.743496i 0.0393504 0.0395164i
\(355\) 0 0
\(356\) −23.9628 + 7.02226i −1.27003 + 0.372179i
\(357\) 0.160421 1.13485i 0.00849039 0.0600625i
\(358\) −18.3820 13.7682i −0.971519 0.727674i
\(359\) 12.9032 0.681005 0.340503 0.940244i \(-0.389403\pi\)
0.340503 + 0.940244i \(0.389403\pi\)
\(360\) 0 0
\(361\) −12.1892 −0.641538
\(362\) 11.0340 + 8.26450i 0.579932 + 0.434372i
\(363\) 1.09461 7.74346i 0.0574521 0.406426i
\(364\) 8.80487 + 30.0459i 0.461501 + 1.57483i
\(365\) 0 0
\(366\) −1.92228 + 1.93039i −0.100479 + 0.100903i
\(367\) 11.7255i 0.612065i −0.952021 0.306032i \(-0.900998\pi\)
0.952021 0.306032i \(-0.0990016\pi\)
\(368\) 15.0737 9.66459i 0.785770 0.503801i
\(369\) −7.70792 + 26.7188i −0.401258 + 1.39093i
\(370\) 0 0
\(371\) 29.3879i 1.52574i
\(372\) −2.29056 15.7259i −0.118760 0.815350i
\(373\) 31.0944i 1.61001i 0.593270 + 0.805004i \(0.297837\pi\)
−0.593270 + 0.805004i \(0.702163\pi\)
\(374\) 0.462407 0.617360i 0.0239105 0.0319229i
\(375\) 0 0
\(376\) 28.0752 + 10.4971i 1.44787 + 0.541346i
\(377\) 39.8653i 2.05317i
\(378\) −19.8515 + 11.0168i −1.02105 + 0.566645i
\(379\) 12.6097 0.647719 0.323860 0.946105i \(-0.395019\pi\)
0.323860 + 0.946105i \(0.395019\pi\)
\(380\) 0 0
\(381\) 1.64428 + 0.232434i 0.0842390 + 0.0119080i
\(382\) −1.95504 + 2.61018i −0.100029 + 0.133549i
\(383\) −1.64428 −0.0840188 −0.0420094 0.999117i \(-0.513376\pi\)
−0.0420094 + 0.999117i \(0.513376\pi\)
\(384\) 1.40785 + 19.5453i 0.0718443 + 0.997416i
\(385\) 0 0
\(386\) −9.53765 + 12.7337i −0.485453 + 0.648130i
\(387\) 32.8742 + 9.48364i 1.67109 + 0.482081i
\(388\) −4.52483 15.4406i −0.229713 0.783876i
\(389\) −37.4889 −1.90076 −0.950381 0.311090i \(-0.899306\pi\)
−0.950381 + 0.311090i \(0.899306\pi\)
\(390\) 0 0
\(391\) 0.958763i 0.0484867i
\(392\) −6.74357 2.52136i −0.340602 0.127348i
\(393\) −6.48486 0.916694i −0.327118 0.0462411i
\(394\) −5.75023 + 7.67714i −0.289692 + 0.386769i
\(395\) 0 0
\(396\) −15.2791 + 0.0643136i −0.767804 + 0.00323188i
\(397\) 19.8820i 0.997849i 0.866646 + 0.498924i \(0.166271\pi\)
−0.866646 + 0.498924i \(0.833729\pi\)
\(398\) 0.716261 + 0.536484i 0.0359029 + 0.0268915i
\(399\) −13.8280 1.95472i −0.692267 0.0978583i
\(400\) 0 0
\(401\) 11.2570i 0.562150i −0.959686 0.281075i \(-0.909309\pi\)
0.959686 0.281075i \(-0.0906910\pi\)
\(402\) −4.09619 4.07899i −0.204300 0.203441i
\(403\) 23.2451 1.15792
\(404\) −0.610382 2.08287i −0.0303676 0.103627i
\(405\) 0 0
\(406\) −27.5142 20.6083i −1.36551 1.02277i
\(407\) 19.5501 0.969065
\(408\) 0.921700 + 0.501407i 0.0456309 + 0.0248233i
\(409\) 16.9007 0.835685 0.417843 0.908519i \(-0.362786\pi\)
0.417843 + 0.908519i \(0.362786\pi\)
\(410\) 0 0
\(411\) 22.6171 + 3.19713i 1.11562 + 0.157703i
\(412\) 22.3250 6.54230i 1.09987 0.322316i
\(413\) −1.32344 −0.0651221
\(414\) −15.1528 + 11.4494i −0.744720 + 0.562709i
\(415\) 0 0
\(416\) −28.5873 2.08287i −1.40161 0.102121i
\(417\) 4.19278 29.6605i 0.205321 1.45248i
\(418\) −7.52248 5.63438i −0.367936 0.275587i
\(419\) 7.21126i 0.352293i 0.984364 + 0.176147i \(0.0563633\pi\)
−0.984364 + 0.176147i \(0.943637\pi\)
\(420\) 0 0
\(421\) 11.3995i 0.555578i −0.960642 0.277789i \(-0.910398\pi\)
0.960642 0.277789i \(-0.0896015\pi\)
\(422\) −9.86851 + 13.1755i −0.480391 + 0.641372i
\(423\) −30.5460 8.81199i −1.48520 0.428454i
\(424\) −25.2001 9.42210i −1.22383 0.457578i
\(425\) 0 0
\(426\) 10.6237 + 10.5791i 0.514722 + 0.512559i
\(427\) 3.43613 0.166286
\(428\) −12.4921 + 3.66080i −0.603830 + 0.176951i
\(429\) 3.12814 22.1290i 0.151028 1.06840i
\(430\) 0 0
\(431\) −3.95028 −0.190278 −0.0951391 0.995464i \(-0.530330\pi\)
−0.0951391 + 0.995464i \(0.530330\pi\)
\(432\) −3.08232 20.5548i −0.148298 0.988943i
\(433\) −20.6509 −0.992420 −0.496210 0.868203i \(-0.665275\pi\)
−0.496210 + 0.868203i \(0.665275\pi\)
\(434\) −12.0165 + 16.0433i −0.576811 + 0.770102i
\(435\) 0 0
\(436\) 9.72494 2.84987i 0.465740 0.136484i
\(437\) −11.6824 −0.558847
\(438\) 20.8538 + 20.7662i 0.996432 + 0.992247i
\(439\) 28.5778i 1.36394i 0.731379 + 0.681971i \(0.238877\pi\)
−0.731379 + 0.681971i \(0.761123\pi\)
\(440\) 0 0
\(441\) 7.33704 + 2.11661i 0.349383 + 0.100791i
\(442\) −0.920070 + 1.22839i −0.0437633 + 0.0584285i
\(443\) 21.9689i 1.04378i −0.853014 0.521888i \(-0.825228\pi\)
0.853014 0.521888i \(-0.174772\pi\)
\(444\) 3.83316 + 26.3167i 0.181914 + 1.24894i
\(445\) 0 0
\(446\) 12.1870 + 9.12810i 0.577069 + 0.432228i
\(447\) 0.924813 6.54230i 0.0437422 0.309440i
\(448\) 16.2157 18.6536i 0.766120 0.881300i
\(449\) 9.00493i 0.424969i 0.977164 + 0.212485i \(0.0681555\pi\)
−0.977164 + 0.212485i \(0.931844\pi\)
\(450\) 0 0
\(451\) 23.6050 1.11152
\(452\) −11.6187 + 3.40483i −0.546496 + 0.160150i
\(453\) 22.6783 + 3.20578i 1.06552 + 0.150621i
\(454\) 14.5298 + 10.8829i 0.681918 + 0.510761i
\(455\) 0 0
\(456\) 6.10960 11.2308i 0.286108 0.525932i
\(457\) −18.5748 −0.868891 −0.434446 0.900698i \(-0.643056\pi\)
−0.434446 + 0.900698i \(0.643056\pi\)
\(458\) 16.9429 + 12.6904i 0.791692 + 0.592982i
\(459\) −1.01560 0.455105i −0.0474040 0.0212425i
\(460\) 0 0
\(461\) −34.2003 −1.59287 −0.796434 0.604726i \(-0.793283\pi\)
−0.796434 + 0.604726i \(0.793283\pi\)
\(462\) 13.6559 + 13.5985i 0.635330 + 0.632662i
\(463\) 7.44471i 0.345985i 0.984923 + 0.172992i \(0.0553436\pi\)
−0.984923 + 0.172992i \(0.944656\pi\)
\(464\) 26.4930 16.9862i 1.22991 0.788564i
\(465\) 0 0
\(466\) 23.6547 + 17.7175i 1.09578 + 0.820748i
\(467\) 7.26161i 0.336027i −0.985785 0.168014i \(-0.946265\pi\)
0.985785 0.168014i \(-0.0537353\pi\)
\(468\) 30.4015 0.127968i 1.40531 0.00591530i
\(469\) 7.29130i 0.336681i
\(470\) 0 0
\(471\) −11.2589 1.59155i −0.518784 0.0733349i
\(472\) 0.424310 1.13485i 0.0195304 0.0522356i
\(473\) 29.0431i 1.33540i
\(474\) 20.1047 20.1895i 0.923437 0.927332i
\(475\) 0 0
\(476\) −0.372179 1.27003i −0.0170588 0.0582116i
\(477\) 27.4178 + 7.90958i 1.25538 + 0.362155i
\(478\) −24.2800 + 32.4163i −1.11054 + 1.48269i
\(479\) −23.3649 −1.06757 −0.533785 0.845620i \(-0.679231\pi\)
−0.533785 + 0.845620i \(0.679231\pi\)
\(480\) 0 0
\(481\) −38.8998 −1.77368
\(482\) −7.84203 + 10.4699i −0.357195 + 0.476891i
\(483\) 23.7190 + 3.35290i 1.07925 + 0.152562i
\(484\) −2.53951 8.66584i −0.115432 0.393902i
\(485\) 0 0
\(486\) 4.93540 + 21.4859i 0.223874 + 0.974618i
\(487\) 7.77068i 0.352123i 0.984379 + 0.176062i \(0.0563358\pi\)
−0.984379 + 0.176062i \(0.943664\pi\)
\(488\) −1.10166 + 2.94648i −0.0498699 + 0.133381i
\(489\) 1.97328 13.9594i 0.0892349 0.631264i
\(490\) 0 0
\(491\) 20.5265i 0.926349i 0.886267 + 0.463174i \(0.153290\pi\)
−0.886267 + 0.463174i \(0.846710\pi\)
\(492\) 4.62820 + 31.7751i 0.208655 + 1.43253i
\(493\) 1.68509i 0.0758928i
\(494\) 14.9678 + 11.2110i 0.673433 + 0.504406i
\(495\) 0 0
\(496\) −9.90447 15.4478i −0.444724 0.693628i
\(497\) 18.9104i 0.848249i
\(498\) −3.97382 + 3.99058i −0.178071 + 0.178822i
\(499\) −26.4958 −1.18611 −0.593057 0.805161i \(-0.702079\pi\)
−0.593057 + 0.805161i \(0.702079\pi\)
\(500\) 0 0
\(501\) −5.29861 + 37.4833i −0.236724 + 1.67463i
\(502\) −1.39759 1.04681i −0.0623776 0.0467212i
\(503\) 26.9943 1.20362 0.601809 0.798640i \(-0.294447\pi\)
0.601809 + 0.798640i \(0.294447\pi\)
\(504\) −15.6277 + 21.0486i −0.696113 + 0.937581i
\(505\) 0 0
\(506\) 12.9032 + 9.66459i 0.573618 + 0.429643i
\(507\) −3.07259 + 21.7361i −0.136459 + 0.965332i
\(508\) 1.84014 0.539249i 0.0816430 0.0239253i
\(509\) −25.8064 −1.14385 −0.571925 0.820306i \(-0.693803\pi\)
−0.571925 + 0.820306i \(0.693803\pi\)
\(510\) 0 0
\(511\) 37.1201i 1.64210i
\(512\) 10.7965 + 19.8855i 0.477144 + 0.878825i
\(513\) −5.54541 + 12.3750i −0.244836 + 0.546368i
\(514\) 21.0596 + 15.7738i 0.928901 + 0.695753i
\(515\) 0 0
\(516\) 39.0953 5.69443i 1.72108 0.250683i
\(517\) 26.9862i 1.18685i
\(518\) 20.1092 26.8478i 0.883547 1.17963i
\(519\) −2.30600 + 16.3131i −0.101222 + 0.716063i
\(520\) 0 0
\(521\) 1.70694i 0.0747826i 0.999301 + 0.0373913i \(0.0119048\pi\)
−0.999301 + 0.0373913i \(0.988095\pi\)
\(522\) −26.6321 + 20.1232i −1.16566 + 0.880768i
\(523\) 24.0790 1.05290 0.526451 0.850206i \(-0.323522\pi\)
0.526451 + 0.850206i \(0.323522\pi\)
\(524\) −7.25732 + 2.12674i −0.317037 + 0.0929071i
\(525\) 0 0
\(526\) −9.54541 + 12.7441i −0.416200 + 0.555669i
\(527\) −0.982561 −0.0428010
\(528\) −16.0390 + 7.35009i −0.698008 + 0.319872i
\(529\) −2.96125 −0.128750
\(530\) 0 0
\(531\) −0.356195 + 1.23472i −0.0154576 + 0.0535823i
\(532\) −15.4752 + 4.53497i −0.670934 + 0.196616i
\(533\) −46.9680 −2.03441
\(534\) 21.5796 21.6706i 0.933840 0.937779i
\(535\) 0 0
\(536\) −6.25229 2.33768i −0.270058 0.100972i
\(537\) 27.8513 + 3.93703i 1.20187 + 0.169895i
\(538\) −9.90447 + 13.2235i −0.427012 + 0.570105i
\(539\) 6.48200i 0.279199i
\(540\) 0 0
\(541\) 16.6989i 0.717941i −0.933349 0.358971i \(-0.883128\pi\)
0.933349 0.358971i \(-0.116872\pi\)
\(542\) 0 0
\(543\) −16.7180 2.36324i −0.717436 0.101416i
\(544\) 1.20837 + 0.0880424i 0.0518086 + 0.00377479i
\(545\) 0 0
\(546\) −27.1717 27.0576i −1.16284 1.15796i
\(547\) −15.5833 −0.666292 −0.333146 0.942875i \(-0.608110\pi\)
−0.333146 + 0.942875i \(0.608110\pi\)
\(548\) 25.3112 7.41738i 1.08124 0.316855i
\(549\) 0.924813 3.20578i 0.0394701 0.136819i
\(550\) 0 0
\(551\) −20.5327 −0.874723
\(552\) −10.4797 + 19.2641i −0.446046 + 0.819935i
\(553\) −35.9376 −1.52822
\(554\) 19.7238 + 14.7732i 0.837984 + 0.627655i
\(555\) 0 0
\(556\) −9.72729 33.1935i −0.412529 1.40772i
\(557\) 2.96772 0.125746 0.0628731 0.998022i \(-0.479974\pi\)
0.0628731 + 0.998022i \(0.479974\pi\)
\(558\) 11.7336 + 15.5289i 0.496724 + 0.657392i
\(559\) 57.7883i 2.44419i
\(560\) 0 0
\(561\) −0.132225 + 0.935386i −0.00558256 + 0.0394920i
\(562\) 14.6850 + 10.9991i 0.619448 + 0.463971i
\(563\) 11.7057i 0.493335i −0.969100 0.246668i \(-0.920664\pi\)
0.969100 0.246668i \(-0.0793356\pi\)
\(564\) −36.3265 + 5.29114i −1.52962 + 0.222797i
\(565\) 0 0
\(566\) 10.5038 14.0236i 0.441507 0.589457i
\(567\) 14.8106 23.5335i 0.621986 0.988314i
\(568\) 16.2157 + 6.06291i 0.680396 + 0.254394i
\(569\) 43.3618i 1.81782i −0.416992 0.908910i \(-0.636916\pi\)
0.416992 0.908910i \(-0.363084\pi\)
\(570\) 0 0
\(571\) −8.18544 −0.342550 −0.171275 0.985223i \(-0.554789\pi\)
−0.171275 + 0.985223i \(0.554789\pi\)
\(572\) −7.25732 24.7650i −0.303444 1.03547i
\(573\) 0.559045 3.95479i 0.0233545 0.165214i
\(574\) 24.2800 32.4163i 1.01343 1.35303i
\(575\) 0 0
\(576\) −13.0388 20.1492i −0.543283 0.839550i
\(577\) 18.9612 0.789367 0.394683 0.918817i \(-0.370854\pi\)
0.394683 + 0.918817i \(0.370854\pi\)
\(578\) −14.3738 + 19.1906i −0.597873 + 0.798222i
\(579\) 2.72729 19.2934i 0.113342 0.801805i
\(580\) 0 0
\(581\) 7.10331 0.294695
\(582\) 13.9636 + 13.9049i 0.578808 + 0.576377i
\(583\) 24.2226i 1.00320i
\(584\) 31.8305 + 11.9012i 1.31716 + 0.492473i
\(585\) 0 0
\(586\) −26.9532 + 35.9853i −1.11343 + 1.48654i
\(587\) 19.9546i 0.823614i −0.911271 0.411807i \(-0.864898\pi\)
0.911271 0.411807i \(-0.135102\pi\)
\(588\) 8.72550 1.27091i 0.359834 0.0524116i
\(589\) 11.9724i 0.493315i
\(590\) 0 0
\(591\) 1.64428 11.6319i 0.0676366 0.478474i
\(592\) 16.5748 + 25.8514i 0.681219 + 1.06248i
\(593\) 27.4465i 1.12709i 0.826085 + 0.563546i \(0.190563\pi\)
−0.826085 + 0.563546i \(0.809437\pi\)
\(594\) 16.3624 9.08050i 0.671356 0.372578i
\(595\) 0 0
\(596\) −2.14558 7.32159i −0.0878863 0.299904i
\(597\) −1.08523 0.153408i −0.0444157 0.00627856i
\(598\) −25.6741 19.2300i −1.04989 0.786375i
\(599\) 13.8858 0.567357 0.283679 0.958919i \(-0.408445\pi\)
0.283679 + 0.958919i \(0.408445\pi\)
\(600\) 0 0
\(601\) −10.7502 −0.438511 −0.219255 0.975667i \(-0.570363\pi\)
−0.219255 + 0.975667i \(0.570363\pi\)
\(602\) −39.8843 29.8736i −1.62556 1.21756i
\(603\) 6.80252 + 1.96241i 0.277020 + 0.0799156i
\(604\) 25.3796 7.43745i 1.03268 0.302626i
\(605\) 0 0
\(606\) 1.88363 + 1.87572i 0.0765173 + 0.0761959i
\(607\) 30.7086i 1.24642i 0.782054 + 0.623211i \(0.214172\pi\)
−0.782054 + 0.623211i \(0.785828\pi\)
\(608\) 1.07279 14.7239i 0.0435073 0.597134i
\(609\) 41.6878 + 5.89296i 1.68928 + 0.238795i
\(610\) 0 0
\(611\) 53.6957i 2.17229i
\(612\) −1.28506 + 0.00540914i −0.0519455 + 0.000218652i
\(613\) 13.3170i 0.537870i 0.963158 + 0.268935i \(0.0866716\pi\)
−0.963158 + 0.268935i \(0.913328\pi\)
\(614\) −8.75683 + 11.6913i −0.353397 + 0.471821i
\(615\) 0 0
\(616\) 20.8439 + 7.79336i 0.839826 + 0.314003i
\(617\) 38.3725i 1.54482i 0.635124 + 0.772410i \(0.280949\pi\)
−0.635124 + 0.772410i \(0.719051\pi\)
\(618\) −20.1047 + 20.1895i −0.808728 + 0.812139i
\(619\) 4.59507 0.184691 0.0923457 0.995727i \(-0.470564\pi\)
0.0923457 + 0.995727i \(0.470564\pi\)
\(620\) 0 0
\(621\) 9.51198 21.2266i 0.381703 0.851794i
\(622\) −4.35620 + 5.81597i −0.174668 + 0.233199i
\(623\) −38.5741 −1.54544
\(624\) 31.9135 14.6248i 1.27756 0.585460i
\(625\) 0 0
\(626\) 13.2886 17.7417i 0.531120 0.709099i
\(627\) 11.3976 + 1.61115i 0.455176 + 0.0643433i
\(628\) −12.6001 + 3.69242i −0.502797 + 0.147344i
\(629\) 1.64428 0.0655617
\(630\) 0 0
\(631\) 40.2097i 1.60072i −0.599518 0.800362i \(-0.704641\pi\)
0.599518 0.800362i \(-0.295359\pi\)
\(632\) 11.5220 30.8165i 0.458322 1.22582i
\(633\) 2.82190 19.9626i 0.112161 0.793444i
\(634\) 7.59037 10.1339i 0.301452 0.402469i
\(635\) 0 0
\(636\) 32.6064 4.74929i 1.29293 0.188321i
\(637\) 12.8975i 0.511018i
\(638\) 22.6783 + 16.9862i 0.897842 + 0.672489i
\(639\) −17.6428 5.08964i −0.697937 0.201343i
\(640\) 0 0
\(641\) 7.56252i 0.298702i 0.988784 + 0.149351i \(0.0477184\pi\)
−0.988784 + 0.149351i \(0.952282\pi\)
\(642\) 11.2497 11.2972i 0.443991 0.445864i
\(643\) 2.47018 0.0974145 0.0487072 0.998813i \(-0.484490\pi\)
0.0487072 + 0.998813i \(0.484490\pi\)
\(644\) 26.5444 7.77877i 1.04599 0.306527i
\(645\) 0 0
\(646\) −0.632684 0.473884i −0.0248926 0.0186447i
\(647\) 30.1474 1.18522 0.592608 0.805491i \(-0.298099\pi\)
0.592608 + 0.805491i \(0.298099\pi\)
\(648\) 15.4315 + 20.2452i 0.606208 + 0.795306i
\(649\) 1.09083 0.0428188
\(650\) 0 0
\(651\) 3.43613 24.3078i 0.134672 0.952697i
\(652\) −4.57804 15.6222i −0.179290 0.611811i
\(653\) 8.42674 0.329764 0.164882 0.986313i \(-0.447276\pi\)
0.164882 + 0.986313i \(0.447276\pi\)
\(654\) −8.75774 + 8.79468i −0.342455 + 0.343899i
\(655\) 0 0
\(656\) 20.0126 + 31.2132i 0.781359 + 1.21867i
\(657\) −34.6318 9.99067i −1.35111 0.389773i
\(658\) 37.0596 + 27.7579i 1.44474 + 1.08212i
\(659\) 13.5764i 0.528863i 0.964404 + 0.264432i \(0.0851843\pi\)
−0.964404 + 0.264432i \(0.914816\pi\)
\(660\) 0 0
\(661\) 1.68509i 0.0655425i −0.999463 0.0327713i \(-0.989567\pi\)
0.999463 0.0327713i \(-0.0104333\pi\)
\(662\) 3.80230 5.07646i 0.147781 0.197302i
\(663\) 0.263094 1.86118i 0.0102177 0.0722821i
\(664\) −2.27740 + 6.09109i −0.0883804 + 0.236380i
\(665\) 0 0
\(666\) −19.6358 25.9871i −0.760872 1.00698i
\(667\) 35.2195 1.36370
\(668\) 12.2928 + 41.9482i 0.475624 + 1.62302i
\(669\) −18.4649 2.61018i −0.713895 0.100916i
\(670\) 0 0
\(671\) −2.83219 −0.109335
\(672\) −6.40392 + 29.5863i −0.247036 + 1.14132i
\(673\) 7.03784 0.271289 0.135644 0.990758i \(-0.456690\pi\)
0.135644 + 0.990758i \(0.456690\pi\)
\(674\) 22.0422 29.4286i 0.849035 1.13355i
\(675\) 0 0
\(676\) 7.12844 + 24.3252i 0.274171 + 0.935584i
\(677\) 41.8298 1.60765 0.803825 0.594866i \(-0.202795\pi\)
0.803825 + 0.594866i \(0.202795\pi\)
\(678\) 10.4631 10.5073i 0.401834 0.403529i
\(679\) 24.8554i 0.953863i
\(680\) 0 0
\(681\) −22.0147 3.11198i −0.843604 0.119251i
\(682\) 9.90447 13.2235i 0.379262 0.506353i
\(683\) 28.2464i 1.08082i 0.841403 + 0.540409i \(0.181730\pi\)
−0.841403 + 0.540409i \(0.818270\pi\)
\(684\) 0.0659099 + 15.6583i 0.00252013 + 0.598712i
\(685\) 0 0
\(686\) 15.5782 + 11.6682i 0.594778 + 0.445492i
\(687\) −25.6709 3.62881i −0.979406 0.138448i
\(688\) 38.4040 24.6230i 1.46414 0.938742i
\(689\) 48.1968i 1.83615i
\(690\) 0 0
\(691\) 24.8633 0.945844 0.472922 0.881104i \(-0.343199\pi\)
0.472922 + 0.881104i \(0.343199\pi\)
\(692\) 5.34994 + 18.2562i 0.203374 + 0.693997i
\(693\) −22.6783 6.54230i −0.861477 0.248521i
\(694\) −12.1322 9.08711i −0.460533 0.344942i
\(695\) 0 0
\(696\) −18.4188 + 33.8580i −0.698164 + 1.28338i
\(697\) 1.98532 0.0751994
\(698\) 13.1663 + 9.86165i 0.498352 + 0.373269i
\(699\) −35.8401 5.06633i −1.35560 0.191626i
\(700\) 0 0
\(701\) 42.6271 1.61000 0.805001 0.593274i \(-0.202165\pi\)
0.805001 + 0.593274i \(0.202165\pi\)
\(702\) −32.5569 + 18.0679i −1.22878 + 0.681928i
\(703\) 20.0354i 0.755650i
\(704\) −13.3656 + 15.3750i −0.503736 + 0.579468i
\(705\) 0 0
\(706\) −24.6244 18.4439i −0.926753 0.694144i
\(707\) 3.35290i 0.126099i
\(708\) 0.213877 + 1.46838i 0.00803798 + 0.0551850i
\(709\) 17.0057i 0.638663i 0.947643 + 0.319331i \(0.103458\pi\)
−0.947643 + 0.319331i \(0.896542\pi\)
\(710\) 0 0
\(711\) −9.67240 + 33.5285i −0.362743 + 1.25742i
\(712\) 12.3673 33.0773i 0.463485 1.23962i
\(713\) 20.5361i 0.769085i
\(714\) 1.14854 + 1.14372i 0.0429830 + 0.0428025i
\(715\) 0 0
\(716\) 31.1688 9.13396i 1.16483 0.341352i
\(717\) 6.94289 49.1152i 0.259287 1.83424i
\(718\) −10.9394 + 14.6053i −0.408257 + 0.545064i
\(719\) −28.6386 −1.06804 −0.534020 0.845472i \(-0.679319\pi\)
−0.534020 + 0.845472i \(0.679319\pi\)
\(720\) 0 0
\(721\) 35.9376 1.33839
\(722\) 10.3341 13.7971i 0.384596 0.513475i
\(723\) 2.24243 15.8634i 0.0833969 0.589965i
\(724\) −18.7093 + 5.48274i −0.695327 + 0.203764i
\(725\) 0 0
\(726\) 7.83689 + 7.80397i 0.290854 + 0.289633i
\(727\) 14.1822i 0.525990i 0.964797 + 0.262995i \(0.0847104\pi\)
−0.964797 + 0.262995i \(0.915290\pi\)
\(728\) −41.4741 15.5068i −1.53713 0.574720i
\(729\) −17.9697 20.1517i −0.665545 0.746357i
\(730\) 0 0
\(731\) 2.44269i 0.0903462i
\(732\) −0.555302 3.81244i −0.0205245 0.140912i
\(733\) 51.7027i 1.90968i 0.297113 + 0.954842i \(0.403976\pi\)
−0.297113 + 0.954842i \(0.596024\pi\)
\(734\) 13.2722 + 9.94095i 0.489885 + 0.366927i
\(735\) 0 0
\(736\) −1.84014 + 25.2558i −0.0678285 + 0.930940i
\(737\) 6.00977i 0.221373i
\(738\) −23.7085 31.3771i −0.872720 1.15501i
\(739\) −16.7493 −0.616133 −0.308067 0.951365i \(-0.599682\pi\)
−0.308067 + 0.951365i \(0.599682\pi\)
\(740\) 0 0
\(741\) −22.6783 3.20578i −0.833108 0.117767i
\(742\) −33.2645 24.9153i −1.22118 0.914669i
\(743\) −13.5649 −0.497649 −0.248825 0.968549i \(-0.580044\pi\)
−0.248825 + 0.968549i \(0.580044\pi\)
\(744\) 19.7423 + 10.7398i 0.723786 + 0.393742i
\(745\) 0 0
\(746\) −35.1961 26.3621i −1.28862 0.965185i
\(747\) 1.91181 6.62713i 0.0699496 0.242474i
\(748\) 0.306764 + 1.04681i 0.0112164 + 0.0382750i
\(749\) −20.1092 −0.734774
\(750\) 0 0
\(751\) 37.3072i 1.36136i 0.732581 + 0.680680i \(0.238316\pi\)
−0.732581 + 0.680680i \(0.761684\pi\)
\(752\) −35.6842 + 22.8791i −1.30127 + 0.834316i
\(753\) 2.11755 + 0.299334i 0.0771676 + 0.0109084i
\(754\) −45.1240 33.7981i −1.64332 1.23086i
\(755\) 0 0
\(756\) 4.36018 31.8103i 0.158578 1.15693i
\(757\) 0.385842i 0.0140237i 0.999975 + 0.00701183i \(0.00223195\pi\)
−0.999975 + 0.00701183i \(0.997768\pi\)
\(758\) −10.6906 + 14.2731i −0.388302 + 0.518423i
\(759\) −19.5501 2.76359i −0.709625 0.100312i
\(760\) 0 0
\(761\) 10.2235i 0.370603i −0.982682 0.185302i \(-0.940674\pi\)
0.982682 0.185302i \(-0.0593262\pi\)
\(762\) −1.65713 + 1.66412i −0.0600314 + 0.0602846i
\(763\) 15.6547 0.566738
\(764\) −1.29699 4.42587i −0.0469235 0.160122i
\(765\) 0 0
\(766\) 1.39403 1.86118i 0.0503685 0.0672471i
\(767\) −2.17047 −0.0783711
\(768\) −23.3171 14.9771i −0.841383 0.540439i
\(769\) 4.34816 0.156799 0.0783994 0.996922i \(-0.475019\pi\)
0.0783994 + 0.996922i \(0.475019\pi\)
\(770\) 0 0
\(771\) −31.9083 4.51052i −1.14915 0.162443i
\(772\) −6.32735 21.5915i −0.227726 0.777096i
\(773\) −21.4326 −0.770878 −0.385439 0.922733i \(-0.625950\pi\)
−0.385439 + 0.922733i \(0.625950\pi\)
\(774\) −38.6056 + 29.1703i −1.38765 + 1.04851i
\(775\) 0 0
\(776\) 21.3135 + 7.96894i 0.765111 + 0.286068i
\(777\) −5.75023 + 40.6782i −0.206288 + 1.45932i
\(778\) 31.7834 42.4340i 1.13949 1.52133i
\(779\) 24.1910i 0.866731i
\(780\) 0 0
\(781\) 15.5867i 0.557737i
\(782\) 1.08523 + 0.812847i 0.0388079 + 0.0290674i
\(783\) 16.7180 37.3072i 0.597451 1.33325i
\(784\) 8.57121 5.49549i 0.306115 0.196267i
\(785\) 0 0
\(786\) 6.53553 6.56310i 0.233115 0.234098i
\(787\) −32.2753 −1.15049 −0.575246 0.817980i \(-0.695094\pi\)
−0.575246 + 0.817980i \(0.695094\pi\)
\(788\) −3.81475 13.0175i −0.135895 0.463729i
\(789\) 2.72951 19.3091i 0.0971733 0.687421i
\(790\) 0 0
\(791\) −18.7031 −0.665006
\(792\) 12.8809 17.3491i 0.457705 0.616473i
\(793\) 5.63533 0.200116
\(794\) −22.5046 16.8561i −0.798660 0.598201i
\(795\) 0 0
\(796\) −1.21450 + 0.355908i −0.0430469 + 0.0126148i
\(797\) 14.4120 0.510498 0.255249 0.966875i \(-0.417843\pi\)
0.255249 + 0.966875i \(0.417843\pi\)
\(798\) 13.9361 13.9949i 0.493332 0.495413i
\(799\) 2.26970i 0.0802961i
\(800\) 0 0
\(801\) −10.3820 + 35.9883i −0.366830 + 1.27158i
\(802\) 12.7420 + 9.54382i 0.449935 + 0.337004i
\(803\) 30.5959i 1.07970i
\(804\) 8.08983 1.17833i 0.285306 0.0415563i
\(805\) 0 0
\(806\) −19.7074 + 26.3113i −0.694162 + 0.926777i
\(807\) 2.83219 20.0354i 0.0996977 0.705280i
\(808\) 2.87511 + 1.07498i 0.101146 + 0.0378177i
\(809\) 27.3297i 0.960860i −0.877033 0.480430i \(-0.840481\pi\)
0.877033 0.480430i \(-0.159519\pi\)
\(810\) 0 0
\(811\) 1.18452 0.0415942 0.0207971 0.999784i \(-0.493380\pi\)
0.0207971 + 0.999784i \(0.493380\pi\)
\(812\) 46.6536 13.6717i 1.63722 0.479784i
\(813\) 0 0
\(814\) −16.5748 + 22.1290i −0.580946 + 0.775622i
\(815\) 0 0
\(816\) −1.34897 + 0.618185i −0.0472235 + 0.0216408i
\(817\) −29.7640 −1.04131
\(818\) −14.3285 + 19.1301i −0.500986 + 0.668867i
\(819\) 45.1240 + 13.0175i 1.57676 + 0.454868i
\(820\) 0 0
\(821\) −16.8535 −0.588191 −0.294095 0.955776i \(-0.595018\pi\)
−0.294095 + 0.955776i \(0.595018\pi\)
\(822\) −22.7938 + 22.8900i −0.795026 + 0.798379i
\(823\) 47.6544i 1.66113i 0.556923 + 0.830564i \(0.311982\pi\)
−0.556923 + 0.830564i \(0.688018\pi\)
\(824\) −11.5220 + 30.8165i −0.401389 + 1.07354i
\(825\) 0 0
\(826\) 1.12202 1.49801i 0.0390401 0.0521225i
\(827\) 11.4476i 0.398073i −0.979992 0.199036i \(-0.936219\pi\)
0.979992 0.199036i \(-0.0637812\pi\)
\(828\) −0.113054 26.8586i −0.00392891 0.933400i
\(829\) 13.6692i 0.474751i 0.971418 + 0.237375i \(0.0762871\pi\)
−0.971418 + 0.237375i \(0.923713\pi\)
\(830\) 0 0
\(831\) −29.8843 4.22441i −1.03667 0.146543i
\(832\) 26.5942 30.5924i 0.921986 1.06060i
\(833\) 0.545173i 0.0188891i
\(834\) 30.0183 + 29.8922i 1.03945 + 1.03508i
\(835\) 0 0
\(836\) 12.7552 3.73790i 0.441149 0.129278i
\(837\) −21.7535 9.74808i −0.751910 0.336943i
\(838\) −8.16250 6.11377i −0.281969 0.211197i
\(839\) −16.7180 −0.577168 −0.288584 0.957455i \(-0.593184\pi\)
−0.288584 + 0.957455i \(0.593184\pi\)
\(840\) 0 0
\(841\) 32.9007 1.13451
\(842\) 12.9032 + 9.66459i 0.444674 + 0.333064i
\(843\) −22.2498 3.14521i −0.766323 0.108327i
\(844\) −6.54685 22.3405i −0.225352 0.768993i
\(845\) 0 0
\(846\) 35.8715 27.1044i 1.23329 0.931870i
\(847\) 13.9498i 0.479321i
\(848\) 32.0298 20.5361i 1.09991 0.705214i
\(849\) −3.00356 + 21.2477i −0.103082 + 0.729220i
\(850\) 0 0
\(851\) 34.3665i 1.17807i
\(852\) −20.9815 + 3.05606i −0.718814 + 0.104699i
\(853\) 7.83055i 0.268113i −0.990974 0.134056i \(-0.957200\pi\)
0.990974 0.134056i \(-0.0428004\pi\)
\(854\) −2.91317 + 3.88939i −0.0996868 + 0.133092i
\(855\) 0 0
\(856\) 6.44725 17.2436i 0.220362 0.589375i
\(857\) 25.7234i 0.878696i −0.898317 0.439348i \(-0.855210\pi\)
0.898317 0.439348i \(-0.144790\pi\)
\(858\) 22.3960 + 22.3019i 0.764587 + 0.761375i
\(859\) −12.5142 −0.426980 −0.213490 0.976945i \(-0.568483\pi\)
−0.213490 + 0.976945i \(0.568483\pi\)
\(860\) 0 0
\(861\) −6.94289 + 49.1152i −0.236613 + 1.67384i
\(862\) 3.34908 4.47136i 0.114070 0.152295i
\(863\) 24.1621 0.822489 0.411244 0.911525i \(-0.365094\pi\)
0.411244 + 0.911525i \(0.365094\pi\)
\(864\) 25.8794 + 13.9376i 0.880435 + 0.474167i
\(865\) 0 0
\(866\) 17.5080 23.3750i 0.594947 0.794315i
\(867\) 4.11021 29.0763i 0.139590 0.987484i
\(868\) −7.97185 27.2032i −0.270582 0.923338i
\(869\) 29.6212 1.00483
\(870\) 0 0
\(871\) 11.9579i 0.405178i
\(872\) −5.01908 + 13.4239i −0.169968 + 0.454591i
\(873\) −23.1892 6.68969i −0.784836 0.226412i
\(874\) 9.90447 13.2235i 0.335024 0.447291i
\(875\) 0 0
\(876\) −41.1855 + 5.99887i −1.39153 + 0.202683i
\(877\) 18.7362i 0.632675i 0.948647 + 0.316337i \(0.102453\pi\)
−0.948647 + 0.316337i \(0.897547\pi\)
\(878\) −32.3475 24.2285i −1.09167 0.817671i
\(879\) 7.70728 54.5227i 0.259960 1.83900i
\(880\) 0 0
\(881\) 45.2764i 1.52540i 0.646752 + 0.762701i \(0.276127\pi\)
−0.646752 + 0.762701i \(0.723873\pi\)
\(882\) −8.61622 + 6.51039i −0.290123 + 0.219216i
\(883\) −32.6703 −1.09944 −0.549722 0.835348i \(-0.685266\pi\)
−0.549722 + 0.835348i \(0.685266\pi\)
\(884\) −0.610382 2.08287i −0.0205294 0.0700547i
\(885\) 0 0
\(886\) 24.8669 + 18.6254i 0.835418 + 0.625734i
\(887\) −24.6883 −0.828953 −0.414477 0.910060i \(-0.636035\pi\)
−0.414477 + 0.910060i \(0.636035\pi\)
\(888\) −33.0379 17.9727i −1.10868 0.603125i
\(889\) 2.96216 0.0993477
\(890\) 0 0
\(891\) −12.2075 + 19.3972i −0.408965 + 0.649831i
\(892\) −20.6644 + 6.05566i −0.691895 + 0.202758i
\(893\) 27.6560 0.925474
\(894\) 6.62123 + 6.59342i 0.221447 + 0.220517i
\(895\) 0 0
\(896\) 7.36640 + 34.1694i 0.246094 + 1.14152i
\(897\) 38.8998 + 5.49884i 1.29883 + 0.183601i
\(898\) −10.1928 7.63446i −0.340137 0.254765i
\(899\) 36.0937i 1.20379i
\(900\) 0 0
\(901\) 2.03726i 0.0678710i
\(902\) −20.0126 + 26.7188i −0.666345 + 0.889639i
\(903\) 60.4302 + 8.54237i 2.01099 + 0.284272i
\(904\) 5.99644 16.0379i 0.199439 0.533414i
\(905\) 0 0
\(906\) −22.8555 + 22.9519i −0.759323 + 0.762526i
\(907\) 15.7502 0.522978 0.261489 0.965206i \(-0.415787\pi\)
0.261489 + 0.965206i \(0.415787\pi\)
\(908\) −24.6370 + 7.21982i −0.817607 + 0.239598i
\(909\) −3.12814 0.902414i −0.103754 0.0299312i
\(910\) 0 0
\(911\) 50.4948 1.67297 0.836483 0.547993i \(-0.184608\pi\)
0.836483 + 0.547993i \(0.184608\pi\)
\(912\) 7.53253 + 16.4371i 0.249427 + 0.544287i
\(913\) −5.85482 −0.193766
\(914\) 15.7478 21.0250i 0.520892 0.695445i
\(915\) 0 0
\(916\) −28.7287 + 8.41889i −0.949224 + 0.278168i
\(917\) −11.6824 −0.385788
\(918\) 1.37617 0.763723i 0.0454203 0.0252066i
\(919\) 22.6311i 0.746530i −0.927725 0.373265i \(-0.878238\pi\)
0.927725 0.373265i \(-0.121762\pi\)
\(920\) 0 0
\(921\) 2.50402 17.7139i 0.0825102 0.583692i
\(922\) 28.9953 38.7117i 0.954909 1.27490i
\(923\) 31.0136i 1.02082i
\(924\) −26.9699 + 3.92831i −0.887245 + 0.129232i
\(925\) 0 0
\(926\) −8.42674 6.31169i −0.276920 0.207415i
\(927\) 9.67240 33.5285i 0.317683 1.10122i
\(928\) −3.23417 + 44.3888i −0.106167 + 1.45713i
\(929\) 45.8021i 1.50272i 0.659893 + 0.751360i \(0.270602\pi\)
−0.659893 + 0.751360i \(0.729398\pi\)
\(930\) 0 0
\(931\) −6.64289 −0.217712
\(932\) −40.1093 + 11.7539i −1.31382 + 0.385013i
\(933\) 1.24566 8.81199i 0.0407809 0.288492i
\(934\) 8.21949 + 6.15645i 0.268950 + 0.201445i
\(935\) 0 0
\(936\) −25.6298 + 34.5203i −0.837736 + 1.12833i
\(937\) −4.77203 −0.155895 −0.0779477 0.996957i \(-0.524837\pi\)
−0.0779477 + 0.996957i \(0.524837\pi\)
\(938\) −8.25310 6.18162i −0.269473 0.201837i
\(939\) −3.79988 + 26.8811i −0.124004 + 0.877230i
\(940\) 0 0
\(941\) 28.5031 0.929174 0.464587 0.885528i \(-0.346203\pi\)
0.464587 + 0.885528i \(0.346203\pi\)
\(942\) 11.3469 11.3948i 0.369702 0.371262i
\(943\) 41.4944i 1.35124i
\(944\) 0.924813 + 1.44241i 0.0301001 + 0.0469466i
\(945\) 0 0
\(946\) 32.8742 + 24.6230i 1.06883 + 0.800562i
\(947\) 59.7387i 1.94125i 0.240606 + 0.970623i \(0.422654\pi\)
−0.240606 + 0.970623i \(0.577346\pi\)
\(948\) 5.80777 + 39.8734i 0.188628 + 1.29503i
\(949\) 60.8779i 1.97618i
\(950\) 0 0
\(951\) −2.17047 + 15.3543i −0.0703823 + 0.497897i
\(952\) 1.75309 + 0.655466i 0.0568181 + 0.0212438i
\(953\) 32.0009i 1.03661i −0.855196 0.518305i \(-0.826563\pi\)
0.855196 0.518305i \(-0.173437\pi\)
\(954\) −32.1980 + 24.3287i −1.04245 + 0.787672i
\(955\) 0 0
\(956\) −16.1076 54.9657i −0.520956 1.77772i
\(957\) −34.3607 4.85720i −1.11072 0.157011i
\(958\) 19.8089 26.4470i 0.639998 0.854463i
\(959\) 40.7446 1.31571
\(960\) 0 0
\(961\) 9.95413 0.321101
\(962\) 32.9795 44.0311i 1.06330 1.41962i
\(963\) −5.41227 + 18.7612i −0.174408 + 0.604570i
\(964\) −5.20247 17.7530i −0.167560 0.571784i
\(965\) 0 0
\(966\) −23.9044 + 24.0052i −0.769111 + 0.772355i
\(967\) 30.7086i 0.987521i 0.869598 + 0.493761i \(0.164378\pi\)
−0.869598 + 0.493761i \(0.835622\pi\)
\(968\) 11.9620 + 4.47248i 0.384472 + 0.143751i
\(969\) 0.958603 + 0.135507i 0.0307948 + 0.00435312i
\(970\) 0 0
\(971\) 54.2279i 1.74025i −0.492827 0.870127i \(-0.664036\pi\)
0.492827 0.870127i \(-0.335964\pi\)
\(972\) −28.5043 12.6294i −0.914277 0.405090i
\(973\) 53.4332i 1.71299i
\(974\) −8.79572 6.58805i −0.281833 0.211095i
\(975\) 0 0
\(976\) −2.40115 3.74503i −0.0768590 0.119876i
\(977\) 11.5621i 0.369905i −0.982748 0.184952i \(-0.940787\pi\)
0.982748 0.184952i \(-0.0592131\pi\)
\(978\) 14.1278 + 14.0684i 0.451757 + 0.449859i
\(979\) 31.7943 1.01615
\(980\) 0 0
\(981\) 4.21337 14.6053i 0.134523 0.466311i
\(982\) −23.2342 17.4025i −0.741432 0.555338i
\(983\) −48.8505 −1.55809 −0.779044 0.626969i \(-0.784295\pi\)
−0.779044 + 0.626969i \(0.784295\pi\)
\(984\) −39.8904 21.7005i −1.27166 0.691785i
\(985\) 0 0
\(986\) 1.90737 + 1.42864i 0.0607432 + 0.0454970i
\(987\) −56.1505 7.93738i −1.78729 0.252650i
\(988\) −25.3796 + 7.43745i −0.807434 + 0.236617i
\(989\) 51.0538 1.62342
\(990\) 0 0
\(991\) 8.77480i 0.278741i 0.990240 + 0.139370i \(0.0445079\pi\)
−0.990240 + 0.139370i \(0.955492\pi\)
\(992\) 25.8827 + 1.88582i 0.821775 + 0.0598747i
\(993\) −1.08727 + 7.69154i −0.0345035 + 0.244084i
\(994\) 21.4049 + 16.0324i 0.678923 + 0.508518i
\(995\) 0 0
\(996\) −1.14794 7.88125i −0.0363740 0.249727i
\(997\) 5.99205i 0.189770i −0.995488 0.0948851i \(-0.969752\pi\)
0.995488 0.0948851i \(-0.0302484\pi\)
\(998\) 22.4633 29.9908i 0.711064 0.949343i
\(999\) 36.4036 + 16.3131i 1.15176 + 0.516122i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 600.2.b.h.251.6 yes 12
3.2 odd 2 inner 600.2.b.h.251.7 yes 12
4.3 odd 2 2400.2.b.g.2351.8 12
5.2 odd 4 600.2.m.e.299.1 24
5.3 odd 4 600.2.m.e.299.24 24
5.4 even 2 600.2.b.g.251.7 yes 12
8.3 odd 2 inner 600.2.b.h.251.8 yes 12
8.5 even 2 2400.2.b.g.2351.7 12
12.11 even 2 2400.2.b.g.2351.6 12
15.2 even 4 600.2.m.e.299.23 24
15.8 even 4 600.2.m.e.299.2 24
15.14 odd 2 600.2.b.g.251.6 yes 12
20.3 even 4 2400.2.m.e.1199.2 24
20.7 even 4 2400.2.m.e.1199.23 24
20.19 odd 2 2400.2.b.h.2351.5 12
24.5 odd 2 2400.2.b.g.2351.5 12
24.11 even 2 inner 600.2.b.h.251.5 yes 12
40.3 even 4 600.2.m.e.299.22 24
40.13 odd 4 2400.2.m.e.1199.1 24
40.19 odd 2 600.2.b.g.251.5 12
40.27 even 4 600.2.m.e.299.3 24
40.29 even 2 2400.2.b.h.2351.6 12
40.37 odd 4 2400.2.m.e.1199.24 24
60.23 odd 4 2400.2.m.e.1199.22 24
60.47 odd 4 2400.2.m.e.1199.3 24
60.59 even 2 2400.2.b.h.2351.7 12
120.29 odd 2 2400.2.b.h.2351.8 12
120.53 even 4 2400.2.m.e.1199.21 24
120.59 even 2 600.2.b.g.251.8 yes 12
120.77 even 4 2400.2.m.e.1199.4 24
120.83 odd 4 600.2.m.e.299.4 24
120.107 odd 4 600.2.m.e.299.21 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
600.2.b.g.251.5 12 40.19 odd 2
600.2.b.g.251.6 yes 12 15.14 odd 2
600.2.b.g.251.7 yes 12 5.4 even 2
600.2.b.g.251.8 yes 12 120.59 even 2
600.2.b.h.251.5 yes 12 24.11 even 2 inner
600.2.b.h.251.6 yes 12 1.1 even 1 trivial
600.2.b.h.251.7 yes 12 3.2 odd 2 inner
600.2.b.h.251.8 yes 12 8.3 odd 2 inner
600.2.m.e.299.1 24 5.2 odd 4
600.2.m.e.299.2 24 15.8 even 4
600.2.m.e.299.3 24 40.27 even 4
600.2.m.e.299.4 24 120.83 odd 4
600.2.m.e.299.21 24 120.107 odd 4
600.2.m.e.299.22 24 40.3 even 4
600.2.m.e.299.23 24 15.2 even 4
600.2.m.e.299.24 24 5.3 odd 4
2400.2.b.g.2351.5 12 24.5 odd 2
2400.2.b.g.2351.6 12 12.11 even 2
2400.2.b.g.2351.7 12 8.5 even 2
2400.2.b.g.2351.8 12 4.3 odd 2
2400.2.b.h.2351.5 12 20.19 odd 2
2400.2.b.h.2351.6 12 40.29 even 2
2400.2.b.h.2351.7 12 60.59 even 2
2400.2.b.h.2351.8 12 120.29 odd 2
2400.2.m.e.1199.1 24 40.13 odd 4
2400.2.m.e.1199.2 24 20.3 even 4
2400.2.m.e.1199.3 24 60.47 odd 4
2400.2.m.e.1199.4 24 120.77 even 4
2400.2.m.e.1199.21 24 120.53 even 4
2400.2.m.e.1199.22 24 60.23 odd 4
2400.2.m.e.1199.23 24 20.7 even 4
2400.2.m.e.1199.24 24 40.37 odd 4